- I’ll post a short video solution to the last daily, but it’s not up yet; I’ll note it here when it is.
- Compute the sum of the following two points on this elliptic curve. $E: y^2 = x^3 + x + 1$ modulo $7$. $ P = (0,1)$ and $Q = (2,2)$. Compute $P+Q$.
- What is $P + \infty$ on this curve?
- What is $-P$?
- Suppose, on the same curve, we want to compute the sum of $Q$ with itself. That means we need to find a tangent line! Compute $Q+Q$.
- Show that if $P=(x,0)$ is a point on an elliptic curve, then $2P = \infty$.
Fall 2023 – Professor Katherine Stange